Question
Find the polynomial having roots at $ 2 $ , $ 6 $ , $ 12 $ , $ 20 $ and $ 30 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^5-70x^4+1708x^3-17544x^2+72000x-86400 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 2 $ | $ x-2 $ |
| $ 6 $ | $ x-6 $ |
| $ 12 $ | $ x-12 $ |
| $ 20 $ | $ x-20 $ |
| $ 30 $ | $ x-30 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-2 \right) \cdot \left( x-6 \right) \cdot \left( x-12 \right) \cdot \left( x-20 \right) \cdot \left( x-30 \right) = x^5-70x^4+1708x^3-17544x^2+72000x-86400 $$This page was created using
Polynomial From Roots Calculator